Earth’s tilt moves back and forth between about 22 and 24.5 degrees

If there is a mean ratio of 5:8 it would be linked to the known variation of Earth’s tilt, which in turn causes variation in the precession and obliquity periods.

Encyclopedia Britannica’s definition says:

*Precession of the equinoxes, motion of the equinoxes along the ecliptic (the plane of Earth’s orbit) caused by the cyclic precession of Earth’s axis of rotation…The projection onto the sky of Earth’s axis of rotation results in two notable points at opposite directions: the north and south celestial poles. Because of precession, these points trace out circles on the sky.*

(Axial precession is another term for ‘precession of the equinoxes’).

Our 2016 unified precession post started with this quote from Wikipedia (bolds added):

*Because of ***apsidal precession** the Earth’s argument of periapsis slowly increases; it takes about **112000 years** for the ellipse to revolve once relative to the fixed stars. The Earth’s **polar axis**, and hence the solstices and equinoxes, precess with a period of about **26000 years** in relation to the fixed stars. These two forms of ‘precession’ **combine** so that it takes about **21000 years** for the ellipse to revolve once relative to the vernal equinox, that is, for the perihelion to return to the same date (given a calendar that tracks the seasons perfectly).

Three linked precessions

In units of 1,000 years:

21 * (16/3) = 112

112 * (3/13) = 25.846~ (near 26)

25.846~ * (13/16) = 21

That was the number theory of the ‘unified precession’ post, i.e. a 3:13:8*2 ratio.

Where might the obliquity period, known to be somewhere near 41,000 years, fit into that?

Referring to the chart (above, right) and converting decimals to whole numbers:

AY – SY = 328 = 109*3, +1

SY – TY = 1417 = 109*13

AY – TY = 1745 (328 + 1417) = 109*16, +1

[327:1417:1744 = 3:13:16]

So that supports the number theory.

Starting out, I just updated the chart to include an entirely theoretical obliquity period of 8/5 times axial precession, linking it to the other known cycles as suggested by my 2016 comment to the unified precession post, here.

That post was a follow-up to: Why Phi? – some Moon-Earth interactions, which showed how:

*The period of 6441 tropical years (6440.75 sidereal years) is one quarter of the Earth’s ‘precession of the equinox’.*

Multiplying by 4: 25764 tropical years = 25763 sidereal years.

The difference of 1 is due to precession.

[NB Wikipedia quotes 25772 years (‘disputed – discuss’) for this precession cycle, but as it’s not a fixed number the question is: what is the mean period? Earth is currently around the mid-point of the tilt variation, moving towards minimum tilt i.e a shorter precession period. Astronoo says 25765 years.]

But then I came across two things: a paper by EPJ van den Heuvel, cited in Wikipedia, and another entry in Wikipedia (see below), that together suggested viable alternative numbers but with the same 5:8 ratio.

On the Precession as a Cause of Pleistocene Variations of the Atlantic Ocean Water Temperatures

— E. P. J. van den Heuvel (1965)

From the summary:

‘The Fourier spectrum (Fig. 8) shows two significant main periods, P1 = 40000 years and P2 = 12825 years*. The first period agrees well with the period of the oscillations of the obliquity of the ecliptic. The second period corresponds very well with the half precession period.’

[*But the specific periods found were: 42857, 39474 and 12825 years]

From Wikipedia – Axial tilt – long term (Wikipedia):

‘For the past 5 million years, Earth’s obliquity has varied between 22° 2′ 33″ and 24° 30′ 16″, with a mean period of 41,040 years. This cycle is a combination of precession and the largest term in the motion of the ecliptic.’

41040:12825 = 16:5 exactly. Since 12825 is the half precession period, the full period ratio is 8:5 as in the chart, but with slightly different numbers.

If this is correct, the 25764y period in the chart would need adjusting by a factor of 225/226:

25764 * (225/226) = 25650 = 2 * 12825

The Wikipedia obliquity period of 41040 years is divisible by 19, so is an exact number of Metonic cycles (2160), as is the revised axial precession of 25650 years (1350). So the alternative period equals a reduction of 6 Metonic cycles of axial precession. The idea of a role for the Moon in Earth’s obliquity has been put forward before.

Of course 225/226 represents less than half a percent of correction, so could be argued to be negligible.

– – –

Now something else has turned up, written around the same time as two Talkshop posts already referred to:

The Secret of the Long Count, by John Martineau

In the ‘Long Count’ section of the article the writer also puts forward an argument for a (mean) 5:8 ratio of obliquity and axial (equinoctial) precession, using some historical context (see below).

So at least one other person has been thinking along the same lines. Note that 2,3,5,8 and 13 are Fibonacci numbers.

– – –

**The Secret of the Long Count**

In the summer of 2012 I visited Carnac, accompanied by Geoff Stray. Howard Crowhurst runs an annual midsummer conference there and we had been invited to speak at the 2012-themed event. Halfway through his presentation, Crowhurst was describing his hunches surrounding megalithic awareness of the 41,000-year cycle, when he casually mentioned a startling fact:

*The 41,000-year cycle very precisely consisted of eight Mayan Suns.*

I did a double take. Eight suns, but five made precession! Startled, I cornered Geoff Stray. He had already come across the eight Suns figure for the obliquity cycle, but not realised the significance of 5:8, while Howard Crowhurst had been unaware of the fact that five Suns gave a value for Precession. We had cracked it.

**One Mayan Sun is 5,125 years.**

**
**Five Suns give the Precessional Cycle

**5 x 5125 = 25,625 years** (current value 25,700 years, 75 years out)

**Eight Suns give the Earth’s Obliquity Cycle.**

**
****8 x 5125 = 41,000 years** (current value 41,040 years, 40 years out)

Five and eight! The two long cycles that most affect the Earth relate as 5:8 and are both encoded by the Long Count. The Maya must have known. No wonder they drew so many pictures of jawbones. Five and eight! The same two numbers displayed by human teeth are the same two numbers as those used by the plants all around us, and these are the same two numbers that connect us with our closest neighbour Venus, and the same two numbers that relate the two long cycles that affect Earth-bound astronomy.

*[emphasis by the author]*

From: The Secret of the Long Count, by John Martineau